1
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Kim DH, Hong S, Kim YS, Kim Y, Lee SW, Pooser RC, Oh K, Lee SY, Lee C, Lim HT. Distributed quantum sensing of multiple phases with fewer photons. Nat Commun 2024; 15:266. [PMID: 38212341 PMCID: PMC10784500 DOI: 10.1038/s41467-023-44204-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/19/2023] [Accepted: 12/04/2023] [Indexed: 01/13/2024] Open
Abstract
Distributed quantum metrology has drawn intense interest as it outperforms the optimal classical counterparts in estimating multiple distributed parameters. However, most schemes so far have required entangled resources consisting of photon numbers equal to or more than the parameter numbers, which is a fairly demanding requirement as the number of nodes increases. Here, we present a distributed quantum sensing scenario in which quantum-enhanced sensitivity can be achieved with fewer photons than the number of parameters. As an experimental demonstration, using a two-photon entangled state, we estimate four phases distributed 3 km away from the central node, resulting in a 2.2 dB sensitivity enhancement from the standard quantum limit. Our results show that the Heisenberg scaling can be achieved even when using fewer photons than the number of parameters. We believe our scheme will open a pathway to perform large-scale distributed quantum sensing with currently available entangled sources.
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Affiliation(s)
- Dong-Hyun Kim
- Center for Quantum Information, Korea Institute of Science and Technology (KIST), Seoul, 02792, Korea
- Department of Physics, Yonsei University, Seoul, 03722, Korea
| | - Seongjin Hong
- Department of Physics, Chung-Ang University, Seoul, 06974, Korea
| | - Yong-Su Kim
- Center for Quantum Information, Korea Institute of Science and Technology (KIST), Seoul, 02792, Korea
- Division of Nanoscience and Technology, KIST School, Korea University of Science and Technology, Seoul, 02792, Korea
| | - Yosep Kim
- Center for Quantum Information, Korea Institute of Science and Technology (KIST), Seoul, 02792, Korea
- Department of Physics, Korea University, Seoul, 02841, Korea
| | - Seung-Woo Lee
- Center for Quantum Information, Korea Institute of Science and Technology (KIST), Seoul, 02792, Korea
| | | | - Kyunghwan Oh
- Department of Physics, Yonsei University, Seoul, 03722, Korea
| | - Su-Yong Lee
- Emerging Science and Technology Directorate, Agency for Defense Development, Daejeon, 34186, Korea
- Weapon Systems Engineering, ADD School, University of Science and Technology, Daejeon, 34060, Korea
| | - Changhyoup Lee
- Korea Research Institute of Standards and Science, Daejeon, 34113, Korea
| | - Hyang-Tag Lim
- Center for Quantum Information, Korea Institute of Science and Technology (KIST), Seoul, 02792, Korea.
- Division of Nanoscience and Technology, KIST School, Korea University of Science and Technology, Seoul, 02792, Korea.
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2
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Le TK, Nguyen HQ, Ho LB. Variational quantum metrology for multiparameter estimation under dephasing noise. Sci Rep 2023; 13:17775. [PMID: 37853037 PMCID: PMC10584960 DOI: 10.1038/s41598-023-44786-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/05/2023] [Accepted: 10/12/2023] [Indexed: 10/20/2023] Open
Abstract
We present a hybrid quantum-classical variational scheme to enhance precision in quantum metrology. In the scheme, both the initial state and the measurement basis in the quantum part are parameterized and optimized via the classical part. It enables the maximization of information gained about the measured quantity. We discuss specific applications to 3D magnetic field sensing under several dephasing noise models. Indeed, we demonstrate its ability to simultaneously estimate all parameters and surpass the standard quantum limit, making it a powerful tool for metrological applications.
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Affiliation(s)
- Trung Kien Le
- Department of Physics, University of California, Santa Barbara, Santa Barbara, USA
- Department of Applied Physics, Stanford University, Stanford, California, 94305, USA
| | - Hung Q Nguyen
- Nano and Energy Center, University of Science, Vietnam National University, Hanoi, 120401, Vietnam
| | - Le Bin Ho
- Frontier Research Institute for Interdisciplinary Sciences, Tohoku University, Sendai, 980-8578, Japan.
- Department of Applied Physics, Graduate School of Engineering, Tohoku University, Sendai, 980-8579, Japan.
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3
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Conlon LO, Lam PK, Assad SM. Multiparameter Estimation with Two-Qubit Probes in Noisy Channels. ENTROPY (BASEL, SWITZERLAND) 2023; 25:1122. [PMID: 37628152 PMCID: PMC10453296 DOI: 10.3390/e25081122] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/31/2023] [Revised: 07/21/2023] [Accepted: 07/24/2023] [Indexed: 08/27/2023]
Abstract
This work compares the performance of single- and two-qubit probes for estimating several phase rotations simultaneously under the action of different noisy channels. We compute the quantum limits for this simultaneous estimation using collective and individual measurements by evaluating the Holevo and Nagaoka-Hayashi Cramér-Rao bounds, respectively. Several quantum noise channels are considered, namely the decohering channel, the amplitude damping channel, and the phase damping channel. For each channel, we find the optimal single- and two-qubit probes. Where possible we demonstrate an explicit measurement strategy that saturates the appropriate bound and we investigate how closely the Holevo bound can be approached through collective measurements on multiple copies of the same probe. We find that under the action of the considered channels, two-qubit probes show enhanced parameter estimation capabilities over single-qubit probes for almost all non-identity channels, i.e., the achievable precision with a single-qubit probe degrades faster with increasing exposure to the noisy environment than that of the two-qubit probe. However, in sufficiently noisy channels, we show that it is possible for single-qubit probes to outperform maximally entangled two-qubit probes. This work shows that, in order to reach the ultimate precision limits allowed by quantum mechanics, entanglement is required in both the state preparation and state measurement stages. It is hoped the tutorial-esque nature of this paper will make it easily accessible.
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Affiliation(s)
- Lorcán O. Conlon
- Centre for Quantum Computation and Communication Technology, Department of Quantum Science, Australian National University, Canberra, ACT 2601, Australia
- Institute of Materials Research and Engineering, Agency for Science Technology and Research (A*STAR), 2 Fusionopolis Way, 08-03 Innovis, Singapore 138634, Singapore
| | - Ping Koy Lam
- Centre for Quantum Computation and Communication Technology, Department of Quantum Science, Australian National University, Canberra, ACT 2601, Australia
- Institute of Materials Research and Engineering, Agency for Science Technology and Research (A*STAR), 2 Fusionopolis Way, 08-03 Innovis, Singapore 138634, Singapore
| | - Syed M. Assad
- Centre for Quantum Computation and Communication Technology, Department of Quantum Science, Australian National University, Canberra, ACT 2601, Australia
- Institute of Materials Research and Engineering, Agency for Science Technology and Research (A*STAR), 2 Fusionopolis Way, 08-03 Innovis, Singapore 138634, Singapore
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4
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Chen H, Chen Y, Yuan H. Information Geometry under Hierarchical Quantum Measurement. PHYSICAL REVIEW LETTERS 2022; 128:250502. [PMID: 35802429 DOI: 10.1103/physrevlett.128.250502] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/31/2022] [Accepted: 05/24/2022] [Indexed: 06/15/2023]
Abstract
In most quantum technologies, measurements need to be performed on the parametrized quantum states to transform the quantum information to classical information. The measurements, however, inevitably distort the information. The characterization of the discrepancy is an important subject in quantum information science, which plays a key role in understanding the difference between the structures of quantum and classical informations. Here we analyze the difference in terms of the Fisher information metric and present a framework that can provide analytical bounds on the discrepancy under hierarchical quantum measurements. Specifically, we present a set of analytical bounds on the difference between the quantum and classical Fisher information metric under hierarchical p-local quantum measurements, which are measurements that can be performed collectively on at most p copies of quantum states. The results can be directly transformed to the precision limit in multiparameter quantum metrology, which leads to characterizations of the trade-off among the precision of different parameters. The framework also provides a coherent picture for various existing results by including them as special cases.
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Affiliation(s)
- Hongzhen Chen
- Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, Hong Kong SAR, People's Republic of China
| | - Yu Chen
- Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, Hong Kong SAR, People's Republic of China
| | - Haidong Yuan
- Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, Hong Kong SAR, People's Republic of China
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5
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Albarelli F, Mazelanik M, Lipka M, Streltsov A, Parniak M, Demkowicz-Dobrzański R. Quantum Asymmetry and Noisy Multimode Interferometry. PHYSICAL REVIEW LETTERS 2022; 128:240504. [PMID: 35776481 DOI: 10.1103/physrevlett.128.240504] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/31/2021] [Revised: 04/13/2022] [Accepted: 05/09/2022] [Indexed: 06/15/2023]
Abstract
Quantum asymmetry is a physical resource that coincides with the amount of coherence between the eigenspaces of a generator responsible for phase encoding in interferometric experiments. We highlight an apparently counterintuitive behavior that the asymmetry may increase as a result of a decrease of coherence inside a degenerate subspace. We intuitively explain and illustrate the phenomena by performing a three-mode single-photon interferometric experiment, where one arm carries the signal and two noisy reference arms have fluctuating phases. We show that the source of the observed sensitivity improvement is the reduction of correlations between these fluctuations and comment on the impact of the effect when moving from the single-photon quantum level to the classical regime. Finally, we also establish the analogy of the effect in the case of entanglement resource theory.
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Affiliation(s)
- Francesco Albarelli
- Faculty of Physics, University of Warsaw, 02-093 Warsaw, Poland
- Dipartimento di Fisica "Aldo Pontremoli", Università degli Studi di Milano, via Celoria 16, 20133 Milan, Italy
| | - Mateusz Mazelanik
- Faculty of Physics, University of Warsaw, 02-093 Warsaw, Poland
- Centre for Quantum Optical Technologies, Centre of New Technologies, University of Warsaw, 02-097 Warsaw, Poland
| | - Michał Lipka
- Centre for Quantum Optical Technologies, Centre of New Technologies, University of Warsaw, 02-097 Warsaw, Poland
| | - Alexander Streltsov
- Centre for Quantum Optical Technologies, Centre of New Technologies, University of Warsaw, 02-097 Warsaw, Poland
| | - Michał Parniak
- Centre for Quantum Optical Technologies, Centre of New Technologies, University of Warsaw, 02-097 Warsaw, Poland
- Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
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6
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Górecki W, Demkowicz-Dobrzański R. Multiple-Phase Quantum Interferometry: Real and Apparent Gains of Measuring All the Phases Simultaneously. PHYSICAL REVIEW LETTERS 2022; 128:040504. [PMID: 35148158 DOI: 10.1103/physrevlett.128.040504] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/04/2021] [Accepted: 12/22/2021] [Indexed: 06/14/2023]
Abstract
We characterize operationally meaningful quantum gains in a paradigmatic model of lossless multiple-phase interferometry and stress the insufficiency of the analysis based solely on the concept of quantum Fisher information. We show that the advantage of the optimal simultaneous estimation scheme amounts to a constant factor improvement when compared with schemes where each phase is estimated separately, which is contrary to widely cited results claiming a better precision scaling in terms of the number of phases involved.
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Affiliation(s)
- Wojciech Górecki
- Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland
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7
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Goldberg AZ, Sánchez-Soto LL, Ferretti H. Intrinsic Sensitivity Limits for Multiparameter Quantum Metrology. PHYSICAL REVIEW LETTERS 2021; 127:110501. [PMID: 34558938 DOI: 10.1103/physrevlett.127.110501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/17/2021] [Revised: 06/30/2021] [Accepted: 07/29/2021] [Indexed: 06/13/2023]
Abstract
The quantum Cramér-Rao bound is a cornerstone of modern quantum metrology, as it provides the ultimate precision in parameter estimation. In the multiparameter scenario, this bound becomes a matrix inequality, which can be cast to a scalar form with a properly chosen weight matrix. Multiparameter estimation thus elicits trade-offs in the precision with which each parameter can be estimated. We show that, if the information is encoded in a unitary transformation, we can naturally choose the weight matrix as the metric tensor linked to the geometry of the underlying algebra su(n), with applications in numerous fields. This ensures an intrinsic bound that is independent of the choice of parametrization.
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Affiliation(s)
- Aaron Z Goldberg
- National Research Council of Canada, 100 Sussex Drive, Ottawa, Ontario K1A 0R6, Canada
- Department of Physics, University of Toronto, 60 St. George Street, Toronto, Ontario M5S 1A7, Canada
| | - Luis L Sánchez-Soto
- Departamento de Óptica, Facultad de Física, Universidad Complutense, 28040 Madrid, Spain
- Max-Planck-Institute für die Physik des Lichts, 91058 Erlangen, Germany
| | - Hugo Ferretti
- Department of Physics, University of Toronto, 60 St. George Street, Toronto, Ontario M5S 1A7, Canada
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8
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Hong S, Ur Rehman J, Kim YS, Cho YW, Lee SW, Jung H, Moon S, Han SW, Lim HT. Quantum enhanced multiple-phase estimation with multi-mode N00N states. Nat Commun 2021; 12:5211. [PMID: 34471118 PMCID: PMC8410777 DOI: 10.1038/s41467-021-25451-4] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/25/2021] [Accepted: 08/11/2021] [Indexed: 02/07/2023] Open
Abstract
Quantum metrology can achieve enhanced sensitivity for estimating unknown parameters beyond the standard quantum limit. Recently, multiple-phase estimation exploiting quantum resources has attracted intensive interest for its applications in quantum imaging and sensor networks. For multiple-phase estimation, the amount of enhanced sensitivity is dependent on quantum probe states, and multi-mode N00N states are known to be a key resource for this. However, its experimental demonstration has been missing so far since generating such states is highly challenging. Here, we report generation of multi-mode N00N states and experimental demonstration of quantum enhanced multiple-phase estimation using the multi-mode N00N states. In particular, we show that the quantum Cramer-Rao bound can be saturated using our two-photon four-mode N00N state and measurement scheme using a 4 × 4 multi-mode beam splitter. Our multiple-phase estimation strategy provides a faithful platform to investigate multiple parameter estimation scenarios.
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Affiliation(s)
- Seongjin Hong
- Center for Quantum Information, Korea Institute of Science and Technology (KIST), Seoul, Korea
| | - Junaid Ur Rehman
- Center for Quantum Information, Korea Institute of Science and Technology (KIST), Seoul, Korea
- Department of Electronics and Information Convergence Engineering, Kyung Hee University, Yongin, Korea
| | - Yong-Su Kim
- Center for Quantum Information, Korea Institute of Science and Technology (KIST), Seoul, Korea
- Division of Nano and Information Technology, KIST School, Korea University of Science and Technology, Seoul, Korea
| | - Young-Wook Cho
- Center for Quantum Information, Korea Institute of Science and Technology (KIST), Seoul, Korea
- Department of Physics, Yonsei University, Seoul, Korea
| | - Seung-Woo Lee
- Center for Quantum Information, Korea Institute of Science and Technology (KIST), Seoul, Korea
| | - Hojoong Jung
- Center for Quantum Information, Korea Institute of Science and Technology (KIST), Seoul, Korea
| | - Sung Moon
- Center for Quantum Information, Korea Institute of Science and Technology (KIST), Seoul, Korea
- Division of Nano and Information Technology, KIST School, Korea University of Science and Technology, Seoul, Korea
| | - Sang-Wook Han
- Center for Quantum Information, Korea Institute of Science and Technology (KIST), Seoul, Korea
- Division of Nano and Information Technology, KIST School, Korea University of Science and Technology, Seoul, Korea
| | - Hyang-Tag Lim
- Center for Quantum Information, Korea Institute of Science and Technology (KIST), Seoul, Korea.
- Division of Nano and Information Technology, KIST School, Korea University of Science and Technology, Seoul, Korea.
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9
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Simultaneous estimation of multiple phases in generalised Mach-Zehnder interferometer. Sci Rep 2021; 11:15669. [PMID: 34341429 PMCID: PMC8329297 DOI: 10.1038/s41598-021-95005-7] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/17/2021] [Accepted: 07/16/2021] [Indexed: 12/02/2022] Open
Abstract
In this work we investigate the problem of simultaneous estimation of phases using generalised three- and four-mode Mach–Zehnder interferometer. In our setup, we assume that the phases are placed in each of the modes in the interferometer, which introduces correlations between estimators of the phases. These correlations prevent simultaneous estimation of all these phases, however we show that we can still obtain the Heisenberg-like scaling of precision of joint estimation of any subset of \documentclass[12pt]{minimal}
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\begin{document}$$d-1$$\end{document}d-1 phases, d being the number of modes, within completely fixed experimental setup, namely with the same initial state and set of measurements. Our estimation scheme can be applied to the task of quantum-enhanced sensing in three-dimensional interferometric configurations.
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10
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Asban S, Dorfman KE, Mukamel S. Interferometric spectroscopy with quantum light: Revealing out-of-time-ordering correlators. J Chem Phys 2021; 154:210901. [PMID: 34240992 DOI: 10.1063/5.0047776] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We survey the inclusion of interferometric elements in nonlinear spectroscopy performed with quantum light. Controlled interference of electromagnetic fields coupled to matter can induce constructive or destructive contributions of microscopic coupling sequences (histories) of matter. Since quantum fields do not commute, quantum light signals are sensitive to the order of light-matter coupling sequences. Matter correlation functions are thus imprinted by different field factors, which depend on that order. We identify the associated quantum information obtained by controlling the weights of different contributing pathways and offer several experimental schemes for recovering it. Nonlinear quantum response functions include out-of-time-ordering matter correlators (OTOCs), which reveal how perturbations spread throughout a quantum system (information scrambling). Their effect becomes most notable when using ultrafast pulse sequences with respect to the path difference induced by the interferometer. OTOCs appear in quantum-informatics studies in other fields, including black hole, high energy, and condensed matter physics.
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Affiliation(s)
- Shahaf Asban
- Department of Chemistry and Physics & Astronomy, University of California, Irvine, California 92697-2025, USA
| | - Konstantin E Dorfman
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, China
| | - Shaul Mukamel
- Department of Chemistry and Physics & Astronomy, University of California, Irvine, California 92697-2025, USA
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11
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Yadin B, Fadel M, Gessner M. Metrological complementarity reveals the Einstein-Podolsky-Rosen paradox. Nat Commun 2021; 12:2410. [PMID: 33893281 PMCID: PMC8065158 DOI: 10.1038/s41467-021-22353-3] [Citation(s) in RCA: 20] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2020] [Accepted: 03/11/2021] [Indexed: 02/02/2023] Open
Abstract
The Einstein-Podolsky-Rosen (EPR) paradox plays a fundamental role in our understanding of quantum mechanics, and is associated with the possibility of predicting the results of non-commuting measurements with a precision that seems to violate the uncertainty principle. This apparent contradiction to complementarity is made possible by nonclassical correlations stronger than entanglement, called steering. Quantum information recognises steering as an essential resource for a number of tasks but, contrary to entanglement, its role for metrology has so far remained unclear. Here, we formulate the EPR paradox in the framework of quantum metrology, showing that it enables the precise estimation of a local phase shift and of its generating observable. Employing a stricter formulation of quantum complementarity, we derive a criterion based on the quantum Fisher information that detects steering in a larger class of states than well-known uncertainty-based criteria. Our result identifies useful steering for quantum-enhanced precision measurements and allows one to uncover steering of non-Gaussian states in state-of-the-art experiments.
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Affiliation(s)
- Benjamin Yadin
- grid.4563.40000 0004 1936 8868School of Mathematical Sciences and Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham, UK ,grid.4991.50000 0004 1936 8948Wolfson College, University of Oxford, Oxford, UK
| | - Matteo Fadel
- grid.6612.30000 0004 1937 0642Department of Physics, University of Basel, Basel, Switzerland
| | - Manuel Gessner
- grid.462844.80000 0001 2308 1657Laboratoire Kastler Brossel, ENS-Université PSL, CNRS, Sorbonne Université, Collège de France, Paris, France
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12
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Abstract
The extraordinary sensitivity of plasmonic sensors is well-known in the optics and photonics community. These sensors exploit simultaneously the enhancement and the localization of electromagnetic fields close to the interface between a metal and a dielectric. This enables, for example, the design of integrated biochemical sensors at scales far below the diffraction limit. Despite their practical realization and successful commercialization, the sensitivity and associated precision of plasmonic sensors are starting to reach their fundamental classical limit given by quantum fluctuations of light-known as the shot-noise limit. To improve the sensing performance of these sensors beyond the classical limit, quantum resources are increasingly being employed. This area of research has become known as "quantum plasmonic sensing", and it has experienced substantial activity in recent years for applications in chemical and biological sensing. This review aims to cover both plasmonic and quantum techniques for sensing, and it shows how they have been merged to enhance the performance of plasmonic sensors beyond traditional methods. We discuss the general framework developed for quantum plasmonic sensing in recent years, covering the basic theory behind the advancements made, and describe the important works that made these advancements. We also describe several key works in detail, highlighting their motivation, the working principles behind them, and their future impact. The intention of the review is to set a foundation for a burgeoning field of research that is currently being explored out of intellectual curiosity and for a wide range of practical applications in biochemistry, medicine, and pharmaceutical research.
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Affiliation(s)
- Changhyoup Lee
- Institute of Theoretical Solid State Physics, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany.,Quantum Universe Center, Korea Institute for Advanced Study, Seoul 02455, Republic of Korea
| | - Benjamin Lawrie
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States
| | - Raphael Pooser
- Quantum Information Science Group, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States
| | - Kwang-Geol Lee
- Department of Physics, Hanyang University, Seoul 04763, Republic of Korea
| | - Carsten Rockstuhl
- Institute of Theoretical Solid State Physics, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany.,Institute of Nanotechnology, Karlsruhe Institute of Technology, 76021Karlsruhe, Germany.,Max Planck School of Photonics, 07745 Jena, Germany
| | - Mark Tame
- Department of Physics, Stellenbosch University, Stellenbosch 7602, South Africa
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13
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Topological protection versus degree of entanglement of two-photon light in photonic topological insulators. Nat Commun 2021; 12:1974. [PMID: 33785744 PMCID: PMC8009886 DOI: 10.1038/s41467-021-22264-3] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/06/2020] [Accepted: 03/03/2021] [Indexed: 11/09/2022] Open
Abstract
Topological insulators combine insulating properties in the bulk with scattering-free transport along edges, supporting dissipationless unidirectional energy and information flow even in the presence of defects and disorder. The feasibility of engineering quantum Hamiltonians with photonic tools, combined with the availability of entangled photons, raises the intriguing possibility of employing topologically protected entangled states in optical quantum computing and information processing. However, while two-photon states built as a product of two topologically protected single-photon states inherit full protection from their single-photon “parents”, a high degree of non-separability may lead to rapid deterioration of the two-photon states after propagation through disorder. In this work, we identify physical mechanisms which contribute to the vulnerability of entangled states in topological photonic lattices. Further, we show that in order to maximize entanglement without sacrificing topological protection, the joint spectral correlation map of two-photon states must fit inside a well-defined topological window of protection. Topological protection of entangled states is a promising avenue for photonic quantum technologies. Here, Tschernig et al. theoretically analyse the impact of disorder on topological protection of entangled two-photon states in periodic and aperiodic topological insulator lattices.
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14
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Qian T, Bringewatt J, Boettcher I, Bienias P, Gorshkov AV. Optimal measurement of field properties with quantum sensor networks. PHYSICAL REVIEW. A 2021; 103:10.1103/PhysRevA.103.L030601. [PMID: 36578467 PMCID: PMC9793443 DOI: 10.1103/physreva.103.l030601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/17/2023]
Abstract
We consider a quantum sensor network of qubit sensors coupled to a field f ( x ; θ ) analytically parameterized by the vector of parameters θ . The qubit sensors are fixed at positions x 1, …, x d . While the functional form of f ( x ; θ ) is known, the parameters θ are not. We derive saturable bounds on the precision of measuring an arbitrary analytic function q( θ ) of these parameters and construct the optimal protocols that achieve these bounds. Our results are obtained from a combination of techniques from quantum information theory and duality theorems for linear programming. They can be applied to many problems, including optimal placement of quantum sensors, field interpolation, and the measurement of functionals of parametrized fields.
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Affiliation(s)
- Timothy Qian
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland College Park, Maryland 20742, USA
- Joint Quantum Institute, NIST/University of Maryland College Park, Maryland 20742, USA
- Montgomery Blair High School, Silver Spring, Maryland 20901, USA
| | - Jacob Bringewatt
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland College Park, Maryland 20742, USA
- Joint Quantum Institute, NIST/University of Maryland College Park, Maryland 20742, USA
| | - Igor Boettcher
- Joint Quantum Institute, NIST/University of Maryland College Park, Maryland 20742, USA
| | - Przemyslaw Bienias
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland College Park, Maryland 20742, USA
- Joint Quantum Institute, NIST/University of Maryland College Park, Maryland 20742, USA
| | - Alexey V Gorshkov
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland College Park, Maryland 20742, USA
- Joint Quantum Institute, NIST/University of Maryland College Park, Maryland 20742, USA
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15
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Hou Z, Jin Y, Chen H, Tang JF, Huang CJ, Yuan H, Xiang GY, Li CF, Guo GC. "Super-Heisenberg" and Heisenberg Scalings Achieved Simultaneously in the Estimation of a Rotating Field. PHYSICAL REVIEW LETTERS 2021; 126:070503. [PMID: 33666488 DOI: 10.1103/physrevlett.126.070503] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/20/2020] [Accepted: 01/25/2021] [Indexed: 06/12/2023]
Abstract
The Heisenberg scaling, which scales as N^{-1} in terms of the number of particles or T^{-1} in terms of the evolution time, serves as a fundamental limit in quantum metrology. Better scalings, dubbed as "super-Heisenberg scaling," however, can also arise when the generator of the parameter involves many-body interactions or when it is time dependent. All these different scalings can actually be seen as manifestations of the Heisenberg uncertainty relations. While there is only one best scaling in the single-parameter quantum metrology, different scalings can coexist for the estimation of multiple parameters, which can be characterized by multiple Heisenberg uncertainty relations. We demonstrate the coexistence of two different scalings via the simultaneous estimation of the magnitude and frequency of a field where the best precisions, characterized by two Heisenberg uncertainty relations, scale as T^{-1} and T^{-2}, respectively (in terms of the standard deviation). We show that the simultaneous saturation of two Heisenberg uncertainty relations can be achieved by the optimal protocol, which prepares the optimal probe state, implements the optimal control, and performs the optimal measurement. The optimal protocol is experimentally implemented on an optical platform that demonstrates the saturation of the two Heisenberg uncertainty relations simultaneously, with up to five controls. As the first demonstration of simultaneously achieving two different Heisenberg scalings, our study deepens the understanding on the connection between the precision limit and the uncertainty relations, which has wide implications in practical applications of multiparameter quantum estimation.
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Affiliation(s)
- Zhibo Hou
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Yan Jin
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Hongzhen Chen
- Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, Hong Kong SAR, China
| | - Jun-Feng Tang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Chang-Jiang Huang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Haidong Yuan
- Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, Hong Kong SAR, China
| | - Guo-Yong Xiang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Chuan-Feng Li
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Guang-Can Guo
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
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Hou Z, Tang JF, Chen H, Yuan H, Xiang GY, Li CF, Guo GC. Zero-trade-off multiparameter quantum estimation via simultaneously saturating multiple Heisenberg uncertainty relations. SCIENCE ADVANCES 2021; 7:7/1/eabd2986. [PMID: 33523843 PMCID: PMC7775755 DOI: 10.1126/sciadv.abd2986] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/12/2020] [Accepted: 11/06/2020] [Indexed: 05/11/2023]
Abstract
Quantum estimation of a single parameter has been studied extensively. Practical applications, however, typically involve multiple parameters, for which the ultimate precision is much less understood. Here, by relating the precision limit directly to the Heisenberg uncertainty relation, we show that to achieve the highest precisions for multiple parameters at the same time requires the saturation of multiple Heisenberg uncertainty relations simultaneously. Guided by this insight, we experimentally demonstrate an optimally controlled multipass scheme, which saturates three Heisenberg uncertainty relations simultaneously and achieves the highest precisions for the estimation of all three parameters in SU(2) operators. With eight controls, we achieve a 13.27-dB improvement in terms of the variance (6.63 dB for the SD) over the classical scheme with the same loss. As an experiment demonstrating the simultaneous achievement of the ultimate precisions for multiple parameters, our work marks an important step in multiparameter quantum metrology with wide implications.
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Affiliation(s)
- Zhibo Hou
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, P. R. China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, P. R. China
| | - Jun-Feng Tang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, P. R. China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, P. R. China
| | - Hongzhen Chen
- Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, Hong Kong
| | - Haidong Yuan
- Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, Hong Kong.
| | - Guo-Yong Xiang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, P. R. China.
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, P. R. China
| | - Chuan-Feng Li
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, P. R. China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, P. R. China
| | - Guang-Can Guo
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, P. R. China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, P. R. China
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17
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Razavian S, Paris MGA, Genoni MG. On the Quantumness of Multiparameter Estimation Problems for Qubit Systems. ENTROPY 2020; 22:e22111197. [PMID: 33286965 PMCID: PMC7712222 DOI: 10.3390/e22111197] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 09/03/2020] [Revised: 10/13/2020] [Accepted: 10/20/2020] [Indexed: 12/03/2022]
Abstract
The estimation of more than one parameter in quantum mechanics is a fundamental problem with relevant practical applications. In fact, the ultimate limits in the achievable estimation precision are ultimately linked with the non-commutativity of different observables, a peculiar property of quantum mechanics. We here consider several estimation problems for qubit systems and evaluate the corresponding quantumnessR, a measure that has been recently introduced in order to quantify how incompatible the parameters to be estimated are. In particular, R is an upper bound for the renormalized difference between the (asymptotically achievable) Holevo bound and the SLD Cramér-Rao bound (i.e., the matrix generalization of the single-parameter quantum Cramér-Rao bound). For all the estimation problems considered, we evaluate the quantumness R and, in order to better understand its usefulness in characterizing a multiparameter quantum statistical model, we compare it with the renormalized difference between the Holevo and the SLD-bound. Our results give evidence that R is a useful quantity to characterize multiparameter estimation problems, as for several quantum statistical model, it is equal to the difference between the bounds and, in general, their behavior qualitatively coincide. On the other hand, we also find evidence that, for certain quantum statistical models, the bound is not in tight, and thus R may overestimate the degree of quantum incompatibility between parameters.
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Affiliation(s)
- Sholeh Razavian
- Faculty of Physics, Azarbaijan Shahid Madani University, Tabriz 5375171379, Iran;
- Quantum Technology Lab, Dipartimento di Fisica “Aldo Pontremoli”, Università degli Studi di Milano, I-20133 Milano, Italy
| | - Matteo G. A. Paris
- Quantum Technology Lab, Dipartimento di Fisica “Aldo Pontremoli”, Università degli Studi di Milano, I-20133 Milano, Italy
- INFN, Sezione di Milano, I-20133 Milano, Italy;
| | - Marco G. Genoni
- Quantum Technology Lab, Dipartimento di Fisica “Aldo Pontremoli”, Università degli Studi di Milano, I-20133 Milano, Italy
- INFN, Sezione di Milano, I-20133 Milano, Italy;
- Correspondence:
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18
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Gessner M, Smerzi A, Pezzè L. Multiparameter squeezing for optimal quantum enhancements in sensor networks. Nat Commun 2020; 11:3817. [PMID: 32733031 PMCID: PMC7393128 DOI: 10.1038/s41467-020-17471-3] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/28/2020] [Accepted: 06/12/2020] [Indexed: 11/09/2022] Open
Abstract
Squeezing currently represents the leading strategy for quantum enhanced precision measurements of a single parameter in a variety of continuous- and discrete-variable settings and technological applications. However, many important physical problems including imaging and field sensing require the simultaneous measurement of multiple unknown parameters. The development of multiparameter quantum metrology is yet hindered by the intrinsic difficulty in finding saturable sensitivity bounds and feasible estimation strategies. Here, we derive the general operational concept of multiparameter squeezing, identifying metrologically useful states and optimal estimation strategies. When applied to spin- or continuous-variable systems, our results generalize widely-used spin- or quadrature-squeezing parameters. Multiparameter squeezing provides a practical and versatile concept that paves the way to the development of quantum-enhanced estimation of multiple phases, gradients, and fields, and for the efficient characterization of multimode quantum states in atomic and optical sensor networks.
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Affiliation(s)
- Manuel Gessner
- Laboratoire Kastler Brossel, ENS-PSL Université, CNRS, Sorbonne Université, Collège de France, 24 Rue Lhomond, 75005, Paris, France.
| | - Augusto Smerzi
- QSTAR, CNR-INO and LENS, Largo Enrico Fermi 2, 50125, Firenze, Italy
| | - Luca Pezzè
- QSTAR, CNR-INO and LENS, Largo Enrico Fermi 2, 50125, Firenze, Italy
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19
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Hou Z, Zhang Z, Xiang GY, Li CF, Guo GC, Chen H, Liu L, Yuan H. Minimal Tradeoff and Ultimate Precision Limit of Multiparameter Quantum Magnetometry under the Parallel Scheme. PHYSICAL REVIEW LETTERS 2020; 125:020501. [PMID: 32701348 DOI: 10.1103/physrevlett.125.020501] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/09/2019] [Accepted: 05/12/2020] [Indexed: 06/11/2023]
Abstract
The precise measurement of a magnetic field is one of the most fundamental and important tasks in quantum metrology. Although extensive studies on quantum magnetometry have been carried out over past decades, the ultimate precision that can be achieved for the estimation of all three components of a magnetic field under the parallel scheme remains unknown. This is largely due to the lack of understandings on the incompatibility of the optimal probe states for the estimation of the three components. Here we provide an approach to characterize the minimal tradeoff among the precisions of multiple parameters that arise from the incompatibility of the optimal probe states, which leads to the identification of the ultimate precision limit for the estimation of all three components of a magnetic field under the parallel scheme. The optimal probe state that achieves the ultimate precision is also explicitly constructed. The obtained precision sets a benchmark on the precision of the multiparameter quantum magnetometry under the parallel scheme, which is of fundamental interest and importance in quantum metrology.
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Affiliation(s)
- Zhibo Hou
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Zhao Zhang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Guo-Yong Xiang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Chuan-Feng Li
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Guang-Can Guo
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Hongzhen Chen
- Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, Hong Kong
| | - Liqiang Liu
- Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, Hong Kong
| | - Haidong Yuan
- Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, Hong Kong
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20
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21
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22
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Kura N, Ueda M. Standard Quantum Limit and Heisenberg Limit in Function Estimation. PHYSICAL REVIEW LETTERS 2020; 124:010507. [PMID: 31976685 DOI: 10.1103/physrevlett.124.010507] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/03/2019] [Indexed: 06/10/2023]
Abstract
Unlike well-established parameter estimation, function estimation faces conceptual and mathematical difficulties despite its enormous potential utility. We establish the fundamental error bounds on function estimation in quantum metrology for a spatially varying phase operator, where various degrees of smooth functions are considered. The error bounds are identified in the cases of the absence and the presence of interparticle entanglement, which correspond to the standard quantum limit and the Heisenberg limit, respectively. Notably, these error bounds can be reached by either position-localized states or wave-number-localized ones. In fact, we show that these error bounds are theoretically optimal for any type of probe states, indicating that quantum metrology on functions is also subject to the Nyquist-Shannon sampling theorem, even if classical detection is replaced by quantum measurement.
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Affiliation(s)
- Naoto Kura
- Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyou-ku, Tokyo 113-0033, Japan
| | - Masahito Ueda
- Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyou-ku, Tokyo 113-0033, Japan
- RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan
- Institute for Physics of Intelligence, University of Tokyo, 7-3-1 Hongo, Bunkyou-ku, Tokyo 113-0033, Japan
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23
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Cimini V, Gianani I, Spagnolo N, Leccese F, Sciarrino F, Barbieri M. Calibration of Quantum Sensors by Neural Networks. PHYSICAL REVIEW LETTERS 2019; 123:230502. [PMID: 31868431 DOI: 10.1103/physrevlett.123.230502] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/30/2019] [Indexed: 06/10/2023]
Abstract
Introducing quantum sensors as a solution to real world problems demands reliability and controllability outside of laboratory conditions. Producers and operators ought to be assumed to have limited resources readily available for calibration, and yet, they should be able to trust the devices. Neural networks are almost ubiquitous for similar tasks for classical sensors: here we show the applications of this technique to calibrating a quantum photonic sensor. This is based on a set of training data, collected only relying on the available probe states, hence reducing overhead. We found that covering finely the parameter space is key to achieving uncertainties close to their ultimate level. This technique has the potential to become the standard approach to calibrate quantum sensors.
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Affiliation(s)
- Valeria Cimini
- Dipartimento di Scienze, Università degli Studi Roma Tre, Via della Vasca Navale 84, 00146, Rome, Italy
| | - Ilaria Gianani
- Dipartimento di Scienze, Università degli Studi Roma Tre, Via della Vasca Navale 84, 00146, Rome, Italy
- Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro, 5, 00185, Rome, Italy
| | - Nicolò Spagnolo
- Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro, 5, 00185, Rome, Italy
| | - Fabio Leccese
- Dipartimento di Scienze, Università degli Studi Roma Tre, Via della Vasca Navale 84, 00146, Rome, Italy
| | - Fabio Sciarrino
- Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro, 5, 00185, Rome, Italy
- Consiglio Nazionale delle Ricerche, Istituto dei sistemi Complessi (CNR-ISC), Via dei Taurini 19, 00185, Rome, Italy
| | - Marco Barbieri
- Dipartimento di Scienze, Università degli Studi Roma Tre, Via della Vasca Navale 84, 00146, Rome, Italy
- Istituto Nazionale di Ottica-CNR, Largo Enrico Fermi 6, 50125, Florence, Italy
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24
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Albarelli F, Friel JF, Datta A. Evaluating the Holevo Cramér-Rao Bound for Multiparameter Quantum Metrology. PHYSICAL REVIEW LETTERS 2019; 123:200503. [PMID: 31809066 DOI: 10.1103/physrevlett.123.200503] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/13/2019] [Revised: 08/26/2019] [Indexed: 06/10/2023]
Abstract
Only with the simultaneous estimation of multiple parameters are the quantum aspects of metrology fully revealed. This is due to the incompatibility of observables. The fundamental bound for multiparameter quantum estimation is the Holevo Cramér-Rao bound (HCRB) whose evaluation has so far remained elusive. For finite-dimensional systems we recast its evaluation as a semidefinite program, with reduced size for rank-deficient states. We show that it also satisfies strong duality. We use this result to study phase and loss estimation in optical interferometry and three-dimensional magnetometry with noisy multiqubit systems. For the former, we show that, in some regimes, it is possible to attain the HCRB with the optimal (single-copy) measurement for phase estimation. For the latter, we show a nontrivial interplay between the HCRB and incompatibility and provide numerical evidence that projective single-copy measurements attain the HCRB in the noiseless 2-qubit case.
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Affiliation(s)
- Francesco Albarelli
- Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - Jamie F Friel
- Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
- EPSRC Centre for Doctoral Training in Diamond Science and Technology, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - Animesh Datta
- Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
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25
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Napoli C, Piano S, Leach R, Adesso G, Tufarelli T. Towards Superresolution Surface Metrology: Quantum Estimation of Angular and Axial Separations. PHYSICAL REVIEW LETTERS 2019; 122:140505. [PMID: 31050483 DOI: 10.1103/physrevlett.122.140505] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/23/2018] [Revised: 01/21/2019] [Indexed: 06/09/2023]
Abstract
We investigate the localization of two incoherent point sources with arbitrary angular and axial separations in the paraxial approximation. By using quantum metrology techniques, we show that a simultaneous estimation of the two separations is achievable by a single quantum measurement, with a precision saturating the ultimate limit stemming from the quantum Cramér-Rao bound. Such a precision is not degraded in the subwavelength regime, thus overcoming the traditional limitations of classical direct imaging derived from Rayleigh's criterion. Our results are qualitatively independent of the point spread function of the imaging system, and quantitatively illustrated in detail for the Gaussian instance. This analysis may have relevant applications in three-dimensional surface measurements.
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Affiliation(s)
- Carmine Napoli
- School of Mathematical Sciences and Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, University Park Campus, Nottingham NG7 2RD, United Kingdom
- Manufacturing Metrology Team, Faculty of Engineering, University of Nottingham, Jubilee Campus, Nottingham NG8 1BB, United Kingdom
| | - Samanta Piano
- Manufacturing Metrology Team, Faculty of Engineering, University of Nottingham, Jubilee Campus, Nottingham NG8 1BB, United Kingdom
| | - Richard Leach
- Manufacturing Metrology Team, Faculty of Engineering, University of Nottingham, Jubilee Campus, Nottingham NG8 1BB, United Kingdom
| | - Gerardo Adesso
- School of Mathematical Sciences and Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, University Park Campus, Nottingham NG7 2RD, United Kingdom
| | - Tommaso Tufarelli
- School of Mathematical Sciences and Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, University Park Campus, Nottingham NG7 2RD, United Kingdom
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26
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Brod DJ, Galvão EF, Viggianiello N, Flamini F, Spagnolo N, Sciarrino F. Witnessing Genuine Multiphoton Indistinguishability. PHYSICAL REVIEW LETTERS 2019; 122:063602. [PMID: 30822072 DOI: 10.1103/physrevlett.122.063602] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/20/2018] [Indexed: 06/09/2023]
Abstract
Bosonic interference is a fundamental physical phenomenon, and it is believed to lie at the heart of quantum computational advantage. It is thus necessary to develop practical tools to witness its presence, both for a reliable assessment of a quantum source and for fundamental investigations. Here we describe how linear interferometers can be used to unambiguously witness genuine n-boson indistinguishability. The amount of violation of the proposed witnesses bounds the degree of multiboson indistinguishability, for which we also provide a novel intuitive model using set theory. We experimentally implement this test to bound the degree of three-photon indistinguishability in states we prepare using parametric down-conversion. Our approach results in a convenient tool for practical photonic applications, and may inspire further fundamental advances based on the operational framework we adopt.
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Affiliation(s)
- Daniel J Brod
- Instituto de Física, Universidade Federal Fluminense, Av. Gal. Milton Tavares de Souza s/n, Niterói, Rio de Janeiro 24210-340, Brazil
| | - Ernesto F Galvão
- Instituto de Física, Universidade Federal Fluminense, Av. Gal. Milton Tavares de Souza s/n, Niterói, Rio de Janeiro 24210-340, Brazil
| | - Niko Viggianiello
- Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 5, I-00185 Roma, Italy
| | - Fulvio Flamini
- Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 5, I-00185 Roma, Italy
| | - Nicolò Spagnolo
- Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 5, I-00185 Roma, Italy
| | - Fabio Sciarrino
- Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 5, I-00185 Roma, Italy
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27
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Abstract
Quantum multiparameter estimation involves estimating multiple parameters simultaneously and can be more precise than estimating them individually. Our interest here is to determine fundamental quantum limits to the achievable multiparameter estimation precision in the presence of noise. We first present a lower bound to the estimation error covariance for a noisy initial probe state evolving through a noiseless quantum channel. We then present a lower bound to the estimation error covariance in the most general form for a noisy initial probe state evolving through a noisy quantum channel. We show conditions and accordingly measurements to attain these estimation precision limits for noisy systems. We see that the Heisenberg precision scaling of 1/N can be achieved with a probe comprising N particles even in the presence of noise. In fact, some noise in the initial probe state or the quantum channel can serve as a feature rather than a bug, since the estimation precision scaling achievable in the presence of noise in the initial state or the channel in some situations is impossible in the absence of noise in the initial state or the channel. However, a lot of noise harms the quantum advantage achievable with N parallel resources, and allows for a best precision scaling of \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
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\setlength{\oddsidemargin}{-69pt}
\begin{document}$${\bf{1}}/\sqrt{{\boldsymbol{N}}}$$\end{document}1/N. Moreover, the Heisenberg precision limit can be beaten with noise in the channel, and we present a super-Heisenberg precision limit with scaling of 1/N2 for optimal amount of noise in the channel, characterized by one-particle evolution operators. Furthermore, using γ-particle evolution operators for the noisy channel, where γ > 1, the best precision scaling attainable is 1/N2γ, which is otherwise known to be only possible using 2γ-particle evolution operators for a noiseless channel.
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28
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Banchi L, Kolthammer WS, Kim MS. Multiphoton Tomography with Linear Optics and Photon Counting. PHYSICAL REVIEW LETTERS 2018; 121:250402. [PMID: 30608836 DOI: 10.1103/physrevlett.121.250402] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/03/2018] [Indexed: 06/09/2023]
Abstract
Determining an unknown quantum state from an ensemble of identical systems is a fundamental, yet experimentally demanding, task in quantum science. Here we study the number of measurement bases needed to fully characterize an arbitrary multimode state containing a definite number of photons, or an arbitrary mixture of such states. We show this task can be achieved using only linear optics and photon counting, which yield a practical though nonuniversal set of projective measurements. We derive the minimum number of measurement settings required and numerically show that this lower bound is saturated with random linear optics configurations, such as when the corresponding unitary transformation is Haar random. Furthermore, we show that for N photons, any unitary 2N design can be used to derive an analytical, though nonoptimal, state reconstruction protocol.
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Affiliation(s)
- Leonardo Banchi
- QOLS, Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom
| | - W Steven Kolthammer
- QOLS, Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom
| | - M S Kim
- QOLS, Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom
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29
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Liu Y, Li J, Cui L, Huo N, Assad SM, Li X, Ou ZY. Loss-tolerant quantum dense metrology with SU(1,1) interferometer. OPTICS EXPRESS 2018; 26:27705-27715. [PMID: 30469832 DOI: 10.1364/oe.26.027705] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/06/2018] [Accepted: 08/13/2018] [Indexed: 05/19/2023]
Abstract
Heisenberg uncertainty relation in quantum mechanics sets the limit on the measurement precision of non-commuting observables in one system, which prevents us from measuring them accurately at the same time. However, quantum entanglement between two systems allows us to infer through Einstein-Podolsky-Rosen correlations two conjugate observables with precision better than what is allowed by Heisenberg uncertainty relation. With the help of the newly developed SU(1,) interferometer, we implement a scheme to jointly measure information encoded in multiple non-commuting observables of an optical field with a signal-to-noise ratio improvement of about 20% over the classical limit on all measured quantities simultaneously. This scheme can be generalized to the joint measurement of information in arbitrary number of non-commuting observables.
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30
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Gessner M, Pezzè L, Smerzi A. Sensitivity Bounds for Multiparameter Quantum Metrology. PHYSICAL REVIEW LETTERS 2018; 121:130503. [PMID: 30312095 DOI: 10.1103/physrevlett.121.130503] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/15/2018] [Indexed: 06/08/2023]
Abstract
We identify precision limits for the simultaneous estimation of multiple parameters in multimode interferometers. Quantum strategies to enhance the multiparameter sensitivity are based on entanglement among particles, modes, or combining both. The maximum attainable sensitivity of particle-separable states defines the multiparameter shot-noise limit, which can be surpassed without mode entanglement. Further enhancements up to the multiparameter Heisenberg limit are possible by adding mode entanglement. Optimal strategies that saturate the precision bounds are provided.
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Affiliation(s)
- Manuel Gessner
- QSTAR, CNR-INO and LENS, Largo Enrico Fermi 2, I-50125 Firenze, Italy
| | - Luca Pezzè
- QSTAR, CNR-INO and LENS, Largo Enrico Fermi 2, I-50125 Firenze, Italy
| | - Augusto Smerzi
- QSTAR, CNR-INO and LENS, Largo Enrico Fermi 2, I-50125 Firenze, Italy
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31
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Branford D, Miao H, Datta A. Fundamental Quantum Limits of Multicarrier Optomechanical Sensors. PHYSICAL REVIEW LETTERS 2018; 121:110505. [PMID: 30265105 DOI: 10.1103/physrevlett.121.110505] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/13/2018] [Revised: 07/27/2018] [Indexed: 06/08/2023]
Abstract
Optomechanical sensors involving multiple optical carriers can experience mechanically mediated interactions causing multimode correlations across the optical fields. One instance is laser-interferometric gravitational wave detectors which introduce multiple carrier frequencies for classical sensing and control purposes. An outstanding question is whether such multicarrier optomechanical sensors outperform their single-carrier counterpart in terms of quantum-limited sensitivity. We show that the best precision is achieved by a single-carrier instance of the sensor. For the current LIGO detection system this precision is already reachable.
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Affiliation(s)
- Dominic Branford
- Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - Haixing Miao
- School of Physics and Astronomy, Institute of Gravitational Wave Astronomy, University of Birmingham, Birmingham B15 2TT, United Kingdom
| | - Animesh Datta
- Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
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32
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Scalable Generation of Multi-mode NOON States for Quantum Multiple-phase Estimation. Sci Rep 2018; 8:11440. [PMID: 30061625 PMCID: PMC6065404 DOI: 10.1038/s41598-018-29828-2] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/04/2017] [Accepted: 07/19/2018] [Indexed: 12/03/2022] Open
Abstract
Multi-mode NOON states have been attracting increasing attentions recently for their abilities of obtaining supersensitive and superresolved measurements for simultaneous multiple-phase estimation. In this paper, four different methods of generating multi-mode NOON states with a high photon number were proposed. The first method is a linear optical approach that makes use of the Fock state filtration to reduce lower-order Fock state terms from the coherent state inputs, which are jointly combined to produce a multi-mode NOON state with the triggering of multi-fold single-photon coincidence detections (SPCD) and appropriate postselection. The other three methods (two linear and one nonlinear) use N-photon Fock states as the inputs and require SPCD triggering only. All of the four methods can theoretically create a multi-mode NOON state with an arbitrary photon number. Comparisons among these four methods were made with respect to their feasibility and efficiency. The first method is experimentally most feasible since it takes considerably fewer photonic operations and, more importantly, requires neither the use of high-N Fock states nor high-degree of nonlinearity.
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33
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Ge W, Jacobs K, Eldredge Z, Gorshkov AV, Foss-Feig M. Distributed Quantum Metrology with Linear Networks and Separable Inputs. PHYSICAL REVIEW LETTERS 2018; 121:043604. [PMID: 30095935 PMCID: PMC6467277 DOI: 10.1103/physrevlett.121.043604] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/20/2017] [Indexed: 06/08/2023]
Abstract
We derive a bound on the ability of a linear-optical network to estimate a linear combination of independent phase shifts by using an arbitrary nonclassical but unentangled input state, thereby elucidating the quantum resources required to obtain the Heisenberg limit with a multiport interferometer. Our bound reveals that while linear networks can generate highly entangled states, they cannot effectively combine quantum resources that are well distributed across multiple modes for the purposes of metrology: In this sense, linear networks endowed with well-distributed quantum resources behave classically. Conversely, our bound shows that linear networks can achieve the Heisenberg limit for distributed metrology when the input photons are concentrated in a small number of input modes, and we present an explicit scheme for doing so.
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Affiliation(s)
- Wenchao Ge
- United States Army Research Laboratory, Adelphi, Maryland 20783, USA
- The Institute for Research in Electronics and Applied Physics (IREAP), College Park, Maryland 20740, USA
| | - Kurt Jacobs
- United States Army Research Laboratory, Adelphi, Maryland 20783, USA
- Department of Physics, University of Massachusetts at Boston, Boston, Massachusetts 02125, USA
- Hearne Institute for Theoretical Physics, Louisiana State University, Baton Rouge, Louisiana 70803, USA
| | - Zachary Eldredge
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
| | - Alexey V Gorshkov
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
| | - Michael Foss-Feig
- United States Army Research Laboratory, Adelphi, Maryland 20783, USA
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
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34
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Backlund MP, Shechtman Y, Walsworth RL. Fundamental Precision Bounds for Three-Dimensional Optical Localization Microscopy with Poisson Statistics. PHYSICAL REVIEW LETTERS 2018; 121:023904. [PMID: 30085695 DOI: 10.1103/physrevlett.121.023904] [Citation(s) in RCA: 27] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/06/2018] [Indexed: 05/23/2023]
Abstract
Point source localization is a problem of persistent interest in optical imaging. In particular, a number of widely used biological microscopy techniques rely on precise three-dimensional localization of single fluorophores. As emitter depth localization is more challenging than lateral localization, considerable effort has been spent on engineering the response of the microscope in a way that reveals increased depth information. Here, we prove the (sub)optimality of these approaches by deriving and comparing to the measurement-independent quantum Cramér-Rao bound (QCRB). We show that existing methods for depth localization with single-objective collection exceed the QCRB, and we gain insight into the bound by proposing an interferometer arrangement that approaches it. We also show that for light collection with two opposed objectives, an established interferometric technique globally reaches the QCRB in all three dimensions simultaneously, and so this represents an interesting case study from the point of view of quantum multiparameter estimation.
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Affiliation(s)
- Mikael P Backlund
- Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02138, USA
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Yoav Shechtman
- Department of Biomedical Engineering, Technion, Israel Institute of Technology, Haifa 32000, Israel
| | - Ronald L Walsworth
- Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02138, USA
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
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35
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Yu X, Zhao X, Shen L, Shao Y, Liu J, Wang X. Maximal quantum Fisher information for phase estimation without initial parity. OPTICS EXPRESS 2018; 26:16292-16302. [PMID: 30119462 DOI: 10.1364/oe.26.016292] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/01/2018] [Accepted: 06/04/2018] [Indexed: 06/08/2023]
Abstract
Mach-Zehnder interferometer is a common device in quantum phase estimation and the photon losses in it are an important issue for achieving a high phase accuracy. Here we thoroughly discuss the precision limit of the phase in the Mach-Zehnder interferometer with a coherent state and a superposition of coherent states as input states. By providing a general analytical expression of quantum Fisher information, the phase-matching condition and optimal initial parity are given. Especially, in the photon loss scenario, the sensitivity behaviors are analyzed and specific strategies are provided to restore the phase accuracies for symmetric and asymmetric losses.
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36
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Symmetric Logarithmic Derivative of Fermionic Gaussian States. ENTROPY 2018; 20:e20070485. [PMID: 33265575 PMCID: PMC7513002 DOI: 10.3390/e20070485] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Subscribe] [Scholar Register] [Received: 05/21/2018] [Revised: 06/16/2018] [Accepted: 06/16/2018] [Indexed: 01/24/2023]
Abstract
In this article, we derive a closed form expression for the symmetric logarithmic derivative of Fermionic Gaussian states. This provides a direct way of computing the quantum Fisher Information for Fermionic Gaussian states. Applications range from quantum Metrology with thermal states to non-equilibrium steady states with Fermionic many-body systems.
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37
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Effects of dipolar interactions on the sensitivity of nonlinear spinor-BEC interterometry. Sci Rep 2018; 8:3218. [PMID: 29459778 PMCID: PMC5818612 DOI: 10.1038/s41598-018-21566-9] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2017] [Accepted: 01/25/2018] [Indexed: 11/09/2022] Open
Abstract
We consider the effects of dipole-dipole interactions on a nonlinear interferometer with spin-1 Bose-Einstein condensates. Compared with the traditional atomic SU(1,1) interferometer, the shot-noise phase sensitivity can be beaten with respect to the input total average number of particles; and the improved sensitivity depends on the effective strength of the dipolar interaction via modifying the trapping geometry. It indicates that the best performance of the interferometer is achieved with highly oblate trap potential. The Bayesian phase estimation strategy is explored to extract the phase information. We show that the Cramér-Rao phase uncertainly bound can saturate, when the ideal dis-entangle scheme is applied. The phase average of the phase sensitivity is also discussed.
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38
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Eldredge Z, Foss-Feig M, Gross JA, Rolston SL, Gorshkov AV. Optimal and secure measurement protocols for quantum sensor networks. PHYSICAL REVIEW. A 2018; 97:10.1103/PhysRevA.97.042337. [PMID: 31093589 PMCID: PMC6513338 DOI: 10.1103/physreva.97.042337] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Studies of quantum metrology have shown that the use of many-body entangled states can lead to an enhancement in sensitivity when compared with unentangled states. In this paper, we quantify the metrological advantage of entanglement in a setting where the measured quantity is a linear function of parameters individually coupled to each qubit. We first generalize the Heisenberg limit to the measurement of nonlocal observables in a quantum network, deriving a bound based on the multiparameter quantum Fisher information. We then propose measurement protocols that can make use of Greenberger-Horne-Zeilinger (GHZ) states or spin-squeezed states and show that in the case of GHZ states the protocol is optimal, i.e., it saturates our bound. We also identify nanoscale magnetic resonance imaging as a promising setting for this technology.
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Affiliation(s)
- Zachary Eldredge
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
| | - Michael Foss-Feig
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
- United States Army Research Laboratory, Adelphi, Maryland 20783, USA
| | - Jonathan A Gross
- Center for Quantum Information and Control, University of New Mexico, Albuquerque, New Mexico 87131, USA
| | - S L Rolston
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
| | - Alexey V Gorshkov
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
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39
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Pezzè L, Ciampini MA, Spagnolo N, Humphreys PC, Datta A, Walmsley IA, Barbieri M, Sciarrino F, Smerzi A. Optimal Measurements for Simultaneous Quantum Estimation of Multiple Phases. PHYSICAL REVIEW LETTERS 2017; 119:130504. [PMID: 29341700 DOI: 10.1103/physrevlett.119.130504] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/10/2017] [Indexed: 06/07/2023]
Abstract
A quantum theory of multiphase estimation is crucial for quantum-enhanced sensing and imaging and may link quantum metrology to more complex quantum computation and communication protocols. In this Letter, we tackle one of the key difficulties of multiphase estimation: obtaining a measurement which saturates the fundamental sensitivity bounds. We derive necessary and sufficient conditions for projective measurements acting on pure states to saturate the ultimate theoretical bound on precision given by the quantum Fisher information matrix. We apply our theory to the specific example of interferometric phase estimation using photon number measurements, a convenient choice in the laboratory. Our results thus introduce concepts and methods relevant to the future theoretical and experimental development of multiparameter estimation.
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Affiliation(s)
- Luca Pezzè
- QSTAR, INO-CNR and LENS, Largo Enrico Fermi 2, I-50125 Firenze, Italy
| | - Mario A Ciampini
- Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 5, I-00185 Roma, Italy
| | - Nicolò Spagnolo
- Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 5, I-00185 Roma, Italy
| | - Peter C Humphreys
- Department of Physics, Clarendon Laboratory, University of Oxford, Oxford OX1 3PU, United Kingdom
| | - Animesh Datta
- Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - Ian A Walmsley
- Department of Physics, Clarendon Laboratory, University of Oxford, Oxford OX1 3PU, United Kingdom
| | - Marco Barbieri
- Dipartimento di Scienze, Università degli Studi Roma Tre, Via della Vasca Navale 84, 00146 Rome, Italy
| | - Fabio Sciarrino
- Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 5, I-00185 Roma, Italy
| | - Augusto Smerzi
- QSTAR, INO-CNR and LENS, Largo Enrico Fermi 2, I-50125 Firenze, Italy
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40
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Su ZE, Li Y, Rohde PP, Huang HL, Wang XL, Li L, Liu NL, Dowling JP, Lu CY, Pan JW. Multiphoton Interference in Quantum Fourier Transform Circuits and Applications to Quantum Metrology. PHYSICAL REVIEW LETTERS 2017; 119:080502. [PMID: 28952770 DOI: 10.1103/physrevlett.119.080502] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/28/2017] [Indexed: 06/07/2023]
Abstract
Quantum Fourier transforms (QFTs) have gained increased attention with the rise of quantum walks, boson sampling, and quantum metrology. Here, we present and demonstrate a general technique that simplifies the construction of QFT interferometers using both path and polarization modes. On that basis, we first observe the generalized Hong-Ou-Mandel effect with up to four photons. Furthermore, we directly exploit number-path entanglement generated in these QFT interferometers and demonstrate optical phase supersensitivities deterministically.
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Affiliation(s)
- Zu-En Su
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Yuan Li
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Peter P Rohde
- Centre for Quantum Software & Information (QSI), Faculty of Engineering & Information Technology, University of Technology Sydney, Sydney, New South Wales 2007, Australia
| | - He-Liang Huang
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Henan Key Laboratory of Quantum Information and Cryptography, Zhengzhou Information Science and Technology Institute, Zhengzhou, Henan 450000, China
| | - Xi-Lin Wang
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Li Li
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Nai-Le Liu
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Jonathan P Dowling
- Hearne Institute for Theoretical Physics and Department of Physics & Astronomy, Louisiana State University, Baton Rouge, Louisiana 70803, USA
| | - Chao-Yang Lu
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Jian-Wei Pan
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
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41
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Beau M, Del Campo A. Nonlinear Quantum Metrology of Many-Body Open Systems. PHYSICAL REVIEW LETTERS 2017; 119:010403. [PMID: 28731775 DOI: 10.1103/physrevlett.119.010403] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/11/2017] [Indexed: 06/07/2023]
Abstract
We introduce general bounds for the parameter estimation error in nonlinear quantum metrology of many-body open systems in the Markovian limit. Given a k-body Hamiltonian and p-body Lindblad operators, the estimation error of a Hamiltonian parameter using a Greenberger-Horne-Zeilinger state as a probe is shown to scale as N^{-[k-(p/2)]}, surpassing the shot-noise limit for 2k>p+1. Metrology equivalence between initial product states and maximally entangled states is established for p≥1. We further show that one can estimate the system-environment coupling parameter with precision N^{-(p/2)}, while many-body decoherence enhances the precision to N^{-k} in the noise-amplitude estimation of a fluctuating k-body Hamiltonian. For the long-range Ising model, we show that the precision of this parameter beats the shot-noise limit when the range of interactions is below a threshold value.
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Affiliation(s)
- M Beau
- Department of Physics, University of Massachusetts, Boston, Massachusetts 02125, USA
| | - A Del Campo
- Department of Physics, University of Massachusetts, Boston, Massachusetts 02125, USA
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42
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Orieux A, Versteegh MAM, Jöns KD, Ducci S. Semiconductor devices for entangled photon pair generation: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2017; 80:076001. [PMID: 28346219 DOI: 10.1088/1361-6633/aa6955] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Entanglement is one of the most fascinating properties of quantum mechanical systems; when two particles are entangled the measurement of the properties of one of the two allows the properties of the other to be instantaneously known, whatever the distance separating them. In parallel with fundamental research on the foundations of quantum mechanics performed on complex experimental set-ups, we assist today with bourgeoning of quantum information technologies bound to exploit entanglement for a large variety of applications such as secure communications, metrology and computation. Among the different physical systems under investigation, those involving photonic components are likely to play a central role and in this context semiconductor materials exhibit a huge potential in terms of integration of several quantum components in miniature chips. In this article we review the recent progress in the development of semiconductor devices emitting entangled photons. We will present the physical processes allowing the generation of entanglement and the tools to characterize it; we will give an overview of major recent results of the last few years and highlight perspectives for future developments.
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Affiliation(s)
- Adeline Orieux
- Sorbonne Universités, UPMC Univ Paris 06, CNRS, Laboratoire d'Informatique de Paris 6 (LIP6), 4 Place Jussieu, 75005 Paris, France. IRIF UMR 8243, Université Paris Diderot, Sorbonne Paris Cité, CNRS, 75013 Paris, France
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43
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Yuan H. Sequential Feedback Scheme Outperforms the Parallel Scheme for Hamiltonian Parameter Estimation. PHYSICAL REVIEW LETTERS 2016; 117:160801. [PMID: 27792361 DOI: 10.1103/physrevlett.117.160801] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/27/2016] [Indexed: 06/06/2023]
Abstract
Measurement and estimation of parameters are essential for science and engineering, where the main quest is to find the highest achievable precision with the given resources and design schemes to attain it. Two schemes, the sequential feedback scheme and the parallel scheme, are usually studied in the quantum parameter estimation. While the sequential feedback scheme represents the most general scheme, it remains unknown whether it can outperform the parallel scheme for any quantum estimation tasks. In this Letter, we show that the sequential feedback scheme has a threefold improvement over the parallel scheme for Hamiltonian parameter estimations on two-dimensional systems, and an order of O(d+1) improvement for Hamiltonian parameter estimation on d-dimensional systems. We also show that, contrary to the conventional belief, it is possible to simultaneously achieve the highest precision for estimating all three components of a magnetic field, which sets a benchmark on the local precision limit for the estimation of a magnetic field.
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Affiliation(s)
- Haidong Yuan
- Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, Hong Kong
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44
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Quantum-enhanced multiparameter estimation in multiarm interferometers. Sci Rep 2016; 6:28881. [PMID: 27381743 PMCID: PMC4933875 DOI: 10.1038/srep28881] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/29/2015] [Accepted: 06/13/2016] [Indexed: 11/30/2022] Open
Abstract
Quantum metrology is the state-of-the-art measurement technology. It uses quantum resources to enhance the sensitivity of phase estimation over that achievable by classical physics. While single parameter estimation theory has been widely investigated, much less is known about the simultaneous estimation of multiple phases, which finds key applications in imaging and sensing. In this manuscript we provide conditions of useful particle (qudit) entanglement for multiphase estimation and adapt them to multiarm Mach-Zehnder interferometry. We theoretically discuss benchmark multimode Fock states containing useful qudit entanglement and overcoming the sensitivity of separable qudit states in three and four arm Mach-Zehnder-like interferometers - currently within the reach of integrated photonics technology.
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45
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Weimann S, Perez-Leija A, Lebugle M, Keil R, Tichy M, Gräfe M, Heilmann R, Nolte S, Moya-Cessa H, Weihs G, Christodoulides DN, Szameit A. Implementation of quantum and classical discrete fractional Fourier transforms. Nat Commun 2016; 7:11027. [PMID: 27006089 PMCID: PMC4814576 DOI: 10.1038/ncomms11027] [Citation(s) in RCA: 65] [Impact Index Per Article: 8.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/15/2015] [Accepted: 02/15/2016] [Indexed: 11/13/2022] Open
Abstract
Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importance of the discrete Fourier transform, implementation of fractional orders of the corresponding discrete operation has been elusive. Here we report classical and quantum optical realizations of the discrete fractional Fourier transform. In the context of classical optics, we implement discrete fractional Fourier transforms of exemplary wave functions and experimentally demonstrate the shift theorem. Moreover, we apply this approach in the quantum realm to Fourier transform separable and path-entangled biphoton wave functions. The proposed approach is versatile and could find applications in various fields where Fourier transforms are essential tools.
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Affiliation(s)
- Steffen Weimann
- Institute of Applied Physics, Abbe School of Photonics, Friedrich-Schiller-Universität Jena, Max-Wien Platz 1, 07743 Jena, Germany
| | - Armando Perez-Leija
- Institute of Applied Physics, Abbe School of Photonics, Friedrich-Schiller-Universität Jena, Max-Wien Platz 1, 07743 Jena, Germany
| | - Maxime Lebugle
- Institute of Applied Physics, Abbe School of Photonics, Friedrich-Schiller-Universität Jena, Max-Wien Platz 1, 07743 Jena, Germany
| | - Robert Keil
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstraße 25, 6020 Innsbruck, Austria
| | - Malte Tichy
- Department of Physics and Astronomy, University of Aarhus, 8000 Aarhus, Denmark
| | - Markus Gräfe
- Institute of Applied Physics, Abbe School of Photonics, Friedrich-Schiller-Universität Jena, Max-Wien Platz 1, 07743 Jena, Germany
| | - René Heilmann
- Institute of Applied Physics, Abbe School of Photonics, Friedrich-Schiller-Universität Jena, Max-Wien Platz 1, 07743 Jena, Germany
| | - Stefan Nolte
- Institute of Applied Physics, Abbe School of Photonics, Friedrich-Schiller-Universität Jena, Max-Wien Platz 1, 07743 Jena, Germany
| | - Hector Moya-Cessa
- INAOE, Coordinacion de Optica, Luis Enrique Erro No. 1, Tonantzintla, Puebla 72840, Mexico
| | - Gregor Weihs
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstraße 25, 6020 Innsbruck, Austria
| | | | - Alexander Szameit
- Institute of Applied Physics, Abbe School of Photonics, Friedrich-Schiller-Universität Jena, Max-Wien Platz 1, 07743 Jena, Germany
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46
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Baumgratz T, Datta A. Quantum Enhanced Estimation of a Multidimensional Field. PHYSICAL REVIEW LETTERS 2016; 116:030801. [PMID: 26849579 DOI: 10.1103/physrevlett.116.030801] [Citation(s) in RCA: 38] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/22/2015] [Indexed: 06/05/2023]
Abstract
We present a framework for the quantum enhanced estimation of multiple parameters corresponding to noncommuting unitary generators. Our formalism provides a recipe for the simultaneous estimation of all three components of a magnetic field. We propose a probe state that surpasses the precision of estimating the three components individually, and we discuss measurements that come close to attaining the quantum limit. Our study also reveals that too much quantum entanglement may be detrimental to attaining the Heisenberg scaling in the estimation of unitarily generated parameters.
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Affiliation(s)
- Tillmann Baumgratz
- Clarendon Laboratory, Department of Physics, University of Oxford, Oxford OX1 3PU, United Kingdom
| | - Animesh Datta
- Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
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47
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48
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Chaboyer Z, Meany T, Helt LG, Withford MJ, Steel MJ. Tunable quantum interference in a 3D integrated circuit. Sci Rep 2015; 5:9601. [PMID: 25915830 PMCID: PMC5386201 DOI: 10.1038/srep09601] [Citation(s) in RCA: 66] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/04/2014] [Accepted: 03/05/2015] [Indexed: 11/09/2022] Open
Abstract
Integrated photonics promises solutions to questions of stability, complexity, and size in quantum optics. Advances in tunable and non-planar integrated platforms, such as laser-inscribed photonics, continue to bring the realisation of quantum advantages in computation and metrology ever closer, perhaps most easily seen in multi-path interferometry. Here we demonstrate control of two-photon interference in a chip-scale 3D multi-path interferometer, showing a reduced periodicity and enhanced visibility compared to single photon measurements. Observed non-classical visibilities are widely tunable, and explained well by theoretical predictions based on classical measurements. With these predictions we extract Fisher information approaching a theoretical maximum. Our results open a path to quantum enhanced phase measurements.
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Affiliation(s)
- Zachary Chaboyer
- Centre for Ultrahigh bandwidth Devices for Optical Systems (CUDOS), MQ Photonics Research Centre, Department of Physics and Astronomy, Macquarie University, NSW 2109, Australia
| | - Thomas Meany
- Centre for Ultrahigh bandwidth Devices for Optical Systems (CUDOS), MQ Photonics Research Centre, Department of Physics and Astronomy, Macquarie University, NSW 2109, Australia
| | - L. G. Helt
- Centre for Ultrahigh bandwidth Devices for Optical Systems (CUDOS), MQ Photonics Research Centre, Department of Physics and Astronomy, Macquarie University, NSW 2109, Australia
| | - Michael J. Withford
- Centre for Ultrahigh bandwidth Devices for Optical Systems (CUDOS), MQ Photonics Research Centre, Department of Physics and Astronomy, Macquarie University, NSW 2109, Australia
| | - M. J. Steel
- Centre for Ultrahigh bandwidth Devices for Optical Systems (CUDOS), MQ Photonics Research Centre, Department of Physics and Astronomy, Macquarie University, NSW 2109, Australia
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Zhang Z, Mouradian S, Wong FNC, Shapiro JH. Entanglement-enhanced sensing in a lossy and noisy environment. PHYSICAL REVIEW LETTERS 2015; 114:110506. [PMID: 25839252 DOI: 10.1103/physrevlett.114.110506] [Citation(s) in RCA: 45] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/24/2014] [Indexed: 06/04/2023]
Abstract
Nonclassical states are essential for optics-based quantum information processing, but their fragility limits their utility for practical scenarios in which loss and noise inevitably degrade, if not destroy, nonclassicality. Exploiting nonclassical states in quantum metrology yields sensitivity advantages over all classical schemes delivering the same energy per measurement interval to the sample being probed. These enhancements, almost without exception, are severely diminished by quantum decoherence. Here, we experimentally demonstrate an entanglement-enhanced sensing system that is resilient to quantum decoherence. We employ entanglement to realize a 20% signal-to-noise ratio improvement over the optimum classical scheme in an entanglement-breaking environment plagued by 14 dB of loss and a noise background 75 dB stronger than the returned probe light. Our result suggests that advantageous quantum-sensing technology could be developed for practical situations.
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Affiliation(s)
- Zheshen Zhang
- Research Laboratory of Electronics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA
| | - Sara Mouradian
- Research Laboratory of Electronics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA
| | - Franco N C Wong
- Research Laboratory of Electronics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA
| | - Jeffrey H Shapiro
- Research Laboratory of Electronics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA
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50
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Relativistic quantum metrology in open system dynamics. Sci Rep 2015; 5:7946. [PMID: 25609187 PMCID: PMC4302316 DOI: 10.1038/srep07946] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/06/2014] [Accepted: 12/16/2014] [Indexed: 11/08/2022] Open
Abstract
Quantum metrology studies the ultimate limit of precision in estimating a physical quantity if quantum strategies are exploited. Here we investigate the evolution of a two-level atom as a detector which interacts with a massless scalar field using the master equation approach for open quantum system. We employ local quantum estimation theory to estimate the Unruh temperature when probed by a uniformly accelerated detector in the Minkowski vacuum. In particular, we evaluate the Fisher information (FI) for population measurement, maximize its value over all possible detector preparations and evolution times, and compare its behavior with that of the quantum Fisher information (QFI). We find that the optimal precision of estimation is achieved when the detector evolves for a long enough time. Furthermore, we find that in this case the FI for population measurement is independent of initial preparations of the detector and is exactly equal to the QFI, which means that population measurement is optimal. This result demonstrates that the achievement of the ultimate bound of precision imposed by quantum mechanics is possible. Finally, we note that the same configuration is also available to the maximum of the QFI itself.
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